Performance Analysis of ML-Based Feedback Carrier Phase Synchronizers for Coded Signals

This paper considers carrier phase recovery in transmission systems with an iteratively decodable error-control code [turbo codes, low-density parity check (LDPC) codes], whose large coding gains enable reliable communication at very low signal-to-noise ratio (SNR). We compare three types of feedback phase synchronizers, which are all based upon the maximum-likelihood (ML) estimation principle: a data-aided (DA) synchronizer, a non-code-aided (NCA) synchronizer, and an iterative code-aided (CA) synchronizer. We introduce a blockwise forward-backward recursive phase estimator, and we show that the mean-square phase error (MSPE) of the NCA synchronizer equals that of the DA synchronizer when the carrier phase is constant and the loop filter gain is the same for both synchronizers. When the signal is affected by phase noise, the NCA synchronizer (as compared with the DA synchronizer) yields a larger MSPE due to phase fluctuations. We also show that, at the normal operating SNR of the considered code, the performance of the CA synchronizer is very close to that of a DA synchronizer that knows all transmitted symbols in advance